Circuit simulator, circuit simulation method and program

ABSTRACT

Characteristics of a circuit element are predicted accurately by taking account not only of the temperature variation due to self-heating of the element but also of temperature variation due to heat transmission from an adjoining heater element. With reference to an electric network supplied from an electric network input unit ( 2 ) and a heat network supplied from a heat network input unit ( 3 ), a simulation unit ( 4 ) determines a first heat generation temperature resulting from the amount of self-heat generation of that element and a second heat generating temperature resulting from the amount of heat flowing into that element from other elements, respectively, for a plurality of elements which make up a semiconductor integrated circuit, calculates the element temperature of that element based on the first and second heat generation temperatures, and then calculates the voltage value and the current value in the element at that element temperature based on previously provided data indicative of temperature dependency of that element.

TECHNICAL FIELD

The present invention relates to a circuit simulator for use in circuitdesigning of semiconductor integrated circuits, and more particularly,to a circuit simulator for performing circuit designing of semiconductorintegrated circuits which comprise a circuit comprised of a plurality ofelements which are connected and at least one of which is a heatgenerating element.

BACKGROUND ART

JP-8-327698-A describes a circuit simulation method which is capable ofmaking a design taking into consideration self-heat generation of acircuit in which a plurality of circuit elements are connected. Thiscircuit simulation method first calculates the magnitude of current andvoltage of each circuit element, which forms part of the circuit, attemperature T which is given when self-heat generation is not taken intoconsideration (first step). Then, the circuit simulation method sensesthe magnitude of current flowing through each circuit element, whichvaries depending on the power consumption of the circuit, calculatestemperature variation ΔT from a variation in power consumption of thecircuit due to this variation in current, and sets the temperature(T+ΔT) to new temperature T (second step). The voltage or current can becalculated taking into consideration the heat generated by the circuitelement by alternately repeating the first and second steps until thecircuit state converges.

JP-11-175576-A in turn discloses a system for verifying a layout using aheat circuit network. This layout verification system first creates acircuit diagram from the result of a layout performed based on logiccircuits, and calculates a current density of each wiring segment usingthe circuit diagram. Next, the system creates a heat circuit from thecircuit diagram, calculates the temperature of each wiring segment usingthe heat circuit, and derives an allowable current density of eachwiring segment based on that temperature. Then, the system compares thecurrent density of each wiring segment derived from the circuit diagramwith the allowable current density of each wiring segment derived fromthe heat circuit for verification.

DISCLOSURE OF THE INVENTION

In recent years, semiconductor integrated circuits have beenincreasingly miniaturized and reduced in size, and as a result, thetemperature rises not only due to a temperature increase caused byself-heat generation of elements which make up a circuit, but also dueto heat transfer from adjoining heat generating elements, leading tochanges in current/voltage characteristics of non-heat generatingelements, thus making it more and more difficult to precisely estimatethe characteristics of circuit elements.

Since neither the simulation method described in JP-8-327698-A nor theverification system described in JP-11-175576-A is configured to performa simulation that takes into consideration the influence of heat betweenheat-generating elements, it is difficult to accurately verify heattransfers between heat-generating elements. In addition, since theverification system described in JP-11-175576-A uses a heat circuitwhich includes a resistor, acting as heat conductance, placed betweenheat flow sources which act as heat-generating elements, the systemfails to precisely represent heat transfers between heat-generatingelements.

It is an object of the present invention to solve the problems describedabove and to provide a circuit simulator, a circuit simulation method,and a program which are capable of precisely predicting characteristicsof circuit elements that take into consideration not only temperaturevariation due to self-heat generation of the elements but alsotemperature variation due to heat transfer from adjoining heatgenerating elements.

To achieve the above object, a first circuit simulator of the presentinvention is characterized by comprising an electric circuit networkinput unit for inputting an electric circuit network that indicates aconnection relation associated with a plurality of elements which makeup a semiconductor integrated circuit, a heat circuit network input unitfor inputting a heat circuit network which is a heat equivalent circuitassociated with the plurality of elements, and a simulation unit thatexecutes an electric circuit simulation for the semiconductor integratedcircuit based on a first element temperature, a first voltage value, afirst current value, and a thermal resistance value, which have been setfor each of the plurality of elements as initial conditions, withreference to the electric circuit network supplied from the electriccircuit network input unit and the heat circuit network supplied fromthe heat circuit network input unit,

wherein the simulation unit calculates a first heat generationtemperature for each of the plurality of elements, caused by the amountof self-heat generation of the pertinent element, based on the firstvoltage value, first current value, and thermal resistance value of thepertinent element, calculates a second heat generation temperaturecaused by the amount of heat flowing from the other element into thepertinent element based on the first voltage value and first currentvalue of the other element and the thermal resistance value of thepertinent element, calculates a second element temperature of thepertinent element based on the first and second heat generationtemperatures and the first element temperature of the pertinent element,and calculates a second voltage value and a second current value at thepertinent element at the second element temperature based on previouslygiven data indicative of temperature dependency of the pertinentelement.

A second circuit simulator of the present invention is characterized bycomprising an electric circuit network input unit for inputting anelectric circuit network that indicates a connection relation associatedwith a plurality of elements which make up a semiconductor integratedcircuit, a heat circuit network input unit for inputting a heat circuitnetwork which is a heat equivalent circuit associated with the pluralityof elements, and a simulation unit that executes an electric circuitsimulation for the semiconductor integrated circuit based on a firstelement temperature, a first voltage value, a first current value, and afirst thermal resistance value, which have been set for each of theplurality of elements as initial conditions, with reference to theelectric circuit network supplied from the electric circuit networkinput unit and the heat circuit network supplied from the heat circuitnetwork input unit,

wherein the simulation unit calculates a first heat generationtemperature for each of the plurality of elements, caused by the amountof self-heat generation of the pertinent element, based on the firstvoltage value, first current value, and first thermal resistance valueof the pertinent element, calculates a second heat generationtemperature caused by the amount of heat flowing from the other elementinto the pertinent element based on the first voltage value and firstcurrent value of the other element and the first thermal resistancevalue of the pertinent element, calculates a second element temperatureof the pertinent element based on the first and second heat generationtemperatures and the first element temperature of the pertinent element,and calculates a second voltage value, a second current value, and asecond thermal resistance value at the pertinent element at the secondelement temperature based on previously given data indicative oftemperature dependency of the pertinent element.

A first circuit simulation method of the present invention is a methodof simulating a semiconductor integrated circuit comprised of aplurality of elements, which comprises the step of:

executing an electric circuit simulation for the semiconductorintegrated circuit based on a first element temperature, a first voltagevalue, a first current value, and a thermal resistance value set asinitial conditions for each of the plurality of elements, with referenceto an electric circuit network that indicates a connection relationassociated with the plurality of elements and a heat circuit networkwhich is a heat equivalent circuit associated with the plurality ofelements,

wherein the step of executing an electric circuit simulation includesthe steps of calculating a first heat generation temperature for each ofthe plurality of elements, caused by the amount of self-heat generationof the pertinent element, based on the first voltage value, firstcurrent value, and thermal resistance value of the pertinent element,calculating a second heat generation temperature caused by the amount ofheat flowing from the other element into the pertinent element based onthe first voltage value and first current value of the other element andthe thermal resistance value of the pertinent element, calculating asecond element temperature of the pertinent element based on the firstand second heat generation temperatures and the first elementtemperature of the pertinent element, and calculating a second voltagevalue and a second current value at the pertinent element at the secondelement temperature based on previously given data indicative oftemperature dependency of the pertinent element.

A second circuit simulation method of the present invention is a methodof simulating a semiconductor integrated circuit comprised of aplurality of elements, which comprises the step of:

executing an electric circuit simulation for the semiconductorintegrated circuit based on a first element temperature, a first voltagevalue, a first current value, and a first thermal resistance value setas initial conditions for each of the plurality of elements, withreference to an electric circuit network that indicates a connectionrelation associated with the plurality of elements and a heat circuitnetwork which is a heat equivalent circuit associated with the pluralityof elements,

wherein the step of executing an electric circuit simulation includesthe steps of calculating a first heat generation temperature for each ofthe plurality of elements, caused by the amount of self-heat generationof the pertinent element, based on the first voltage value, firstcurrent value, and first thermal resistance value of the pertinentelement, calculating a second heat generation temperature caused by theamount of heat flowing from the other element into the pertinent elementbased on the first voltage value and first current value of the otherelement and the first thermal resistance value of the pertinent element,calculating a second element temperature of the pertinent element basedon the first and second heat generation temperatures and the firstelement temperature of the pertinent element, and calculating a secondvoltage value, a second current value, and a second thermal resistancevalue at the pertinent element at the second element temperature basedon previously given data indicative of temperature dependency of thepertinent element.

A first program of the present invention is a program for causing acomputer to execute processing for executing an electric circuitsimulation for a semiconductor integrated circuit based on a firstelement temperature, a first voltage value, a first current value, and athermal resistance value set as initial conditions for each of aplurality of elements which make up the semiconductor integratedcircuit, with reference to an electric circuit network that indicates aconnection relation associated with the plurality of elements and a heatcircuit network which is a heat equivalent circuit associated with theplurality of elements,

wherein the processing of executing an electric circuit simulationincludes processing of calculating a first heat generation temperaturefor each of the plurality of elements, caused by the amount of self-heatgeneration of the pertinent element, based on the first voltage value,first current value, and thermal resistance value of the pertinentelement, calculating a second heat generation temperature caused by theamount of heat flowing from the other element into the pertinent elementbased on the first voltage value and first current value of the otherelement and the thermal resistance value of the pertinent element,calculating a second element temperature of the pertinent element basedon the first and second heat generation temperatures and the firstelement temperature of the pertinent element, and calculating a secondvoltage value and a second current value at the pertinent element at thesecond element temperature based on previously given data indicative oftemperature dependency of the pertinent element.

A second program of the present invention is a program for causing acomputer to execute processing of executing an electric circuitsimulation for a semiconductor integrated circuit based on a firstelement temperature, a first voltage value, a first current value, and afirst thermal resistance value set as initial conditions for each of aplurality of elements which make up the semiconductor integratedcircuit, with reference to an electric circuit network that indicates aconnection relation associated with the plurality of elements and a heatcircuit network which is a heat equivalent circuit associated with theplurality of elements,

wherein the processing of executing an electric circuit simulationincludes processing of calculating a first heat generation temperaturefor each of the plurality of elements, caused by the amount of self-heatgeneration of the pertinent element, based on the first voltage value,first current value, and first thermal resistance value of the pertinentelement, calculating a second heat generation temperature caused by theamount of heat flowing from the other element into the pertinent elementbased on the first voltage value and first current value of the otherelement and the first thermal resistance value of the pertinent element,calculating a second element temperature of the pertinent element basedon the first and second heat generation temperatures and the firstelement temperature of the pertinent element, and calculating a secondvoltage value, a second current value, and a second thermal resistancevalue at the pertinent element at the second element temperature basedon previously given data indicative of temperature dependency of thepertinent element.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 A block diagram showing the configuration of a main portion of acircuit simulator which is a first exemplary embodiment of the presentinvention.

FIG. 2 A flow chart showing a processing procedure for an electriccircuit simulation performed in the circuit simulator shown in FIG. 1.

FIG. 3 A flow chart showing another processing procedure for an electriccircuit simulation performed in the circuit simulator shown in FIG. 1.

FIG. 4 A circuit diagram showing an exemplary current source element.

FIG. 5 A circuit diagram showing an exemplary voltage controlled currentsource element.

FIG. 6 A block diagram showing the configuration of a main portion of acircuit simulator which is a second exemplary embodiment of the presentinvention.

FIG. 7 A flow chart showing a processing procedure for an electriccircuit simulation performed in the circuit simulator shown in FIG. 6.

DESCRIPTION OF REFERENCE NUMERALS

-   1, 11 Initial Condition Input Units-   2, 12 Electric Circuit Network Input Units-   3 Heat Circuit Network Input Unit-   4, 14 Simulation Units-   5, 15 Output Units-   13 Layout Input Unit-   16 Heat Circuit Network Conversion Unit

BEST MODE FOR CARRYING OUT THE INVENTION

Next, embodiments of the present invention will be described withreference to the drawings.

First Exemplary Embodiment

FIG. 1 is a block diagram showing the configuration of a main portion ofa circuit simulator which is a first exemplary embodiment of the presentinvention.

The circuit simulator of this embodiment is a simulator implemented by acomputer system which is operated by a program, and is used, forexample, for designing semiconductor integrated circuits. The mainportion of this circuit simulator comprises initial condition input unit1, electric circuit network input unit 2, heat circuit network inputunit 3, simulation unit 4, and output unit 5, as shown in FIG. 1.

Electric circuit network input unit 2 supplies simulation unit 4 with anelectric circuit network of a semiconductor integrated circuit which issubjected to a simulation. The electric circuit network is a circuitcomprised of a plurality of elements which are connected, where at leastone of the elements that forms part of the circuit is a heat-generatingelement. The electric circuit network is a circuit which is designed inunits of circuit elements, for example, transistors, resistors and thelike, and may be provided from an external computer device or created bythe simulator. If the electric circuit network is created by thesimulator, an application for creating the electric circuit network thathas been previously prepared (installed in a storage unit, not shown) isrun by a user through a manipulation unit (not shown) such as a keyboardto create an arbitrary electric circuit network.

Heat circuit network input unit 3 supplies simulation unit 4 with a heatcircuit network of a semiconductor integrated circuit which is subjectedto simulation. A creating method that has been used in existing heatcircuit network methods is applied to create the heat circuit network. Aheat circuit network is a heat equivalent circuit which is created insuch a manner that: an object is defined as a part of a semiconductorintegrated circuit which causes a heat transfer; the object is replacedwith a thermal resistance which connects between nodes; and the thermalresistance between nodes (° C./W), temperature (° C.), and heat flow (W)are regarded as resistance (Q), voltage (V), and current (A),respectively. Like the electric circuit network, this heat circuitnetwork may be provided from an external computer device or created bythe simulator.

Initial condition input unit 1 supplies simulation unit 4 with initialconditions which have been set by the user through a manipulation unit,not shown. Parameters set as the initial conditions include the number Nof elements which make up a circuit, temperature T, voltage V, currentI, thermal resistance Rth, voltage convergence determination conditionεv, current convergence determination condition εi, coefficients n, mindicating where an element is positioned in the N elements of thecircuit, and variable k indicative of the number of repetitions.

Simulation unit 4 performs an electric circuit simulation for asemiconductor integrated circuit with reference to the electric circuitnetwork supplied from electric circuit network input unit 2 and the heatcircuit network supplied from heat circuit network input unit 3, andsupplies the result to output unit 5. Output unit 5, which is a displaydevice, for example, LCD (Liquid Crystal Display) or the like, providesthe user with the simulation result supplied from simulation unit 4.

FIG. 2 shows a processing procedure for an electric circuit simulationperformed in the circuit simulator of this embodiment. In the following,an electric circuit simulation will be described specifically withreference to FIG. 2.

First, initial conditions are set for executing the electric circuitsimulation (step 101). Specifically, the number of elements isdesignated by N; the temperature, voltage, current, and thermalresistance of an n-th element are designated by T(n, k), V(n, k), I(n,k), and Rth(n), respectively; the voltage and current of an m-th elementare designated by V(m, k) and I(m, k), respectively; a voltageconvergence determination condition is designated by εv; and currentconvergence determination condition is designated by εi. Then, variablek is set to zero, and coefficients n, m are respectively set to one.Coefficients n, m are respectively in a range of one or more to N orless.

After setting the initial conditions, self-heat generation amount Qs(n,k) in the n-th element is calculated on the basis of voltage value V(n,k) and current value (n, k) in the n-th element (step 102), andself-heat generation temperature ΔTs(n, k) at the n-th element iscalculated on the basis of that self-heat generation amount Qs(n, k) andthermal resistance value Rth(n) in the n-th element (step 103). Further,simultaneously with this processing at steps 102, 103, or sequentially,heat amount Qi(n, m, k) which flows from the m-th element into the n-thelement is calculated on the basis of voltage value V(m, k) and currentvalue I(m, k) in the m-th element (step 104). Then, a countable sum iscalculated in a range where variable m of heat amount Qi(n, m, k)changes from one to n−1, and in a range where variable m changes fromn+1 to N, and heat generation temperature ΔTi(n, m, k) at the n-thelement, caused by the amount of heat flowing from the m-th element tothe n-th element, is calculated on the basis of the countable sum andthermal resistance value Rth(n) in the n-th element (step 105).

Next, temperature T(n, k), self-heat generation temperature ΔTs(n, k),and heat generation temperature ΔTi(n, m, k) of the n-th element areadded to designate the resulting value as element temperature T(n, k+1)of the n-th element (step 106). Then, new voltage value V(n, k+1) andcurrent value I(n, k+1) are calculated in the n-th element at elementtemperature T(n, k+1) (step 107), and the value of coefficient n iscompared with the value of the number N of elements (step 108). Here,new voltage value V(n, k+1) and current value I(n, k+1) in the n-thelement are calculated on the basis of data indicative of previouslygiven temperature dependency (voltage/current characteristics includingthe temperature) of the n-th element.

When it is determined at step 108 that the value of coefficient n isless than number N of elements, coefficient n is incremented by one toproduce new coefficient n, followed by a transition to step 102 and step104 (step 109). When it is determined at step 108 that coefficient n isequal to or more than number N of elements, a countable sum of thedifference between voltage value V(n, k+1) calculated at step 107 andvoltage value V(n, k) in the range of coefficient n from one to N isdesignated as voltage variation EV, and a countable sum of thedifference between current value I(n, k+1) calculated at step 107 andcurrent value I(n, k) in the range of coefficient n from one to N isdesignated as current variation EI (step 110). Then, voltage variationEV is compared with voltage convergence determination condition εv,while current variation EI is compared with current convergencedetermination condition εi, respectively (step 111).

When the value of EV is determined to be larger than the value of εV, orwhen the value of EI is determined to be larger than the value of εi atstep 111, the value of variable k is incremented by one to produce newvariable k, followed by a transition to step 102 and step 104 (step112). When it is determined at step 111 that the value of EV is equal toor less than the value of εv and the value of EI is equal to or lessthan the value of εi, the simulation processing is terminated.

In the foregoing procedure for simulation processing, processing atsteps 102-107 is repeatedly executed until n≧N is satisfied at step 108after step 101 has been executed. Then, after step 110 has beenexecuted, processing at steps 102-110 is repeatedly executed whilechanging each value of voltage value V(n, k) and current value I(n, k)until both EV and EI are determined to be equal to or less than thevalues of the convergence determination conditions at step 111. Throughsuch repeated processing, a voltage, a current, and a temperature can becalculated taking into consideration the influence by respectiveself-heat generation of a plurality of elements which make up thecircuit, and heat generation between the elements.

According to the circuit simulator of this embodiment, for each of aplurality of elements which make up a circuit, the simulator cancalculate a temperature variation of the element due to its self-heatgeneration, and a temperature variation of the element due to heattransfer from other heat generating elements, so that thecurrent/voltage characteristics of the element can be precisely definedon the basis of these temperature variations. The circuit simulator ofthis embodiment enables a precise simulation of a small semiconductorintegrated circuit, and contributes to a reduction in the number oftimes of re-works and a saving in development cost.

The circuit simulator of this embodiment is an example of the presentinvention, and can be modified in configuration and operation asappropriate. For example, when a heat circuit network is generated fromlayout data, a step (113 in FIG. 3) may be added, before step 101 isexecuted, for deriving thermal resistance value Rth(n) in an n-thelement using the element shape of the n-th element on the layout data,as shown in FIG. 3. In this way, since thermal resistance value Rth(n)at the n-th element is derived from the element shape of the layoutdata, a seamless design can be implemented, for example, across maskfabrication and a circuit design.

Alternatively, at step 104, the distance between the n-th element andm-th element is calculated on the basis of the layout data, and heatamount Qi(n, m, k) flowing from the m-th element into the n-th elementmay be derived on the basis of the distance between the elements and onthe basis of voltage value V(m, k) and current value I(m, k) in the m-thelement. In this event, a seamless design can also be implemented, forexample, across mask fabrication and a circuit design.

Alternatively, heat amount Qi(n, m, k) may be represented by Qi(n, m,k)=A×[V(m, k)×I(m, k)], using coefficient A. In this event, coefficientA may depend on time. According to the use of time-dependent coefficientA, the voltage/current characteristics of the element can be simulatedtaking into consideration the transient response of heat (time transientresponse characteristic).

Further, given current source element 20 having one end grounded asshown in FIG. 4, coefficient A may be represented by current gain a ofthe current source element when heat amount Qi(n, m, k) is calculatedfor this current source element 20. Specifically, when the values ofvoltage and current at an m-th element are given by voltage value V(m,k) and current value I(m, k), respectively, self-heat generation amountQs(m, k) of the m-th element is given by:

Qs(m, k)=V(m, k)×I(m, k),

and heat amount Qi(n, m, k) is given by:

Qi(n, m, k)=A×Qs(m, k)

Then, as heat amount Qi(n, m, k) is replaced with the current to producevariable Ic(n, m, k), and self-heat generation amount Qs(m, k) isreplaced with the current to produce variable Ic(m, k), the followingrelationship is established:

Ic(n, m, k)=α×Ic(m, k)

Based on these relationships, coefficient A can be represented bycurrent gain α of the current source element. In this way, a heatcircuit network and an electric circuit network can be precisely andsimultaneously simulated using the electric circuit simulator. Thereason for the above will be briefly described below.

The current/voltage characteristics of a semiconductor device depend onthe temperature and time. For simulating the current/voltagecharacteristics of a semiconductor device taking into consideration thetemperature and time, it is necessary to simultaneously simulate a heatcircuit network and an electric circuit network in an electric circuitsimulator. An existing heat simulator based on a finite element methodcan calculate the temperature but cannot simulate the voltage/currentcharacteristics. Since the electric circuit simulator performs asimulation in conformity with basic laws of electricity (Ohm's law,Kirchhoff's law, Joule's law and the like), it can simultaneouslysimulate an electric circuit network and a heat circuit network. Since aheat circuit network can be converted to an electric circuit network,temperature can be converted to voltage; heat can be converted tocurrent; and thermal resistance can be converted to a resistance.Further, as an object of heat transfer is converted to a current source,the current source can be represented by a function of frequency, thusmaking it possible to simultaneously simulate a heat circuit network andan electric circuit network, including the time which is the inverse offrequency. In this way, the electric circuit simulator of thisembodiment can precisely simulate the voltage/current characteristics ofan element taking into consideration the transient response of heat.

Also, heat amount Qi(n, m, k) may be represented by Qi(n, m, k)=B×[T(m,k)−T(m, 0)] using coefficient B. In this event, coefficient B may alsodepend on the time. By using a coefficient depending on time, thevoltage/current characteristics of an element can be simulated takinginto consideration the transient response of heat (time transientresponse characteristic).

Further, when a voltage controlled current source element as shown inFIG. 5, to which current Inm (corresponding to a heat amount) flowingfrom an m-th element to an n-th element and voltage Vc(m, k) areapplied, is given and when heat amount Qi(n, m, k) is calculated forthis voltage controlled current source element, coefficient B may berepresented by transconductance g of the voltage controlled currentsource element. Specifically, when the temperature of the m-th elementis designated by T(m, k), heat amount Qi(n, m, k) flowing from the m-thelement to the n-th element is given by:

Qi(n, m, k)=B×T(m, k)

Then, the following relationship is established:

Ic(n, m, k)=g×Ic(m, k)

where Ic(n, m, k) is a variable in which Qi(n, m, k) is replaced with acurrent, and Vc(m, k) indicates the value of ΔT, which is the magnitudeof variation in T(m, k), replaced by the voltage. Based on theserelationships, coefficient B can be represented by transconductance g ofthe voltage controlled current source element. In this way, a heatcircuit network and an electric circuit network can be simultaneouslyand precisely simulated using the electric circuit simulator.

Second Exemplary Embodiment

FIG. 6 is a block diagram showing the configuration of a main portion ofa circuit simulator which is a second exemplary embodiment of thepresent invention.

The circuit simulator of this embodiment is a simulator implemented by acomputer system which is operated by a program, and is used, forexample, for designing semiconductor integrated circuits. The mainportion of this circuit simulator comprises initial condition input unit11, electric circuit network input unit 12, layout input unit 13,simulation unit 14, and output unit 15, and neat circuit networkconversion unit 16, as shown in FIG. 6. Electric circuit network inputunit 12 and output unit 15 are the same as those shown in FIG. 1.

Initial condition input unit 11 supplies simulation unit 4 with initialconditions which have been set by the user through a manipulation unit,not shown. Parameters set as the initial conditions include the number Nof elements which make up a circuit, temperature T, voltage V, currentI, thermal resistance Rth, voltage convergence determination conditionεV, thermal resistance convergence determination condition εr, currentconvergence determination condition εi, coefficients n, m indicatingwhere an element is positioned in the N elements of the circuit, andvariable k indicative of the number or repetitions.

Layout input unit 13 supplies simulation unit 14 with layout data of asemiconductor integrated circuit which is subjected to a simulation. Thelayout data represents a circuit diagram which includes placement ofunit cells which define elements, wires and the like which make up asemiconductor integrated circuit, and may be provided from an externalcomputer device or created by the simulator.

Heat circuit network conversion unit 16 converts the layout data createdby layout input unit 13 to a heat circuit network. In the conversionfrom layout data to a heat circuit network, a portion (object) whichcauses a heat transfer is replaced with a thermal resistance whichconnects between nodes, and the thermal resistance between nodes (°C./W), temperature (° C.), and heat flow (W) are regarded as resistance(Q), voltage (V), and current (A), respectively, to create a heatequivalent circuit.

Simulation unit 14 performs an electric circuit simulation for asemiconductor integrated circuit with reference to an electric circuitnetwork supplied from electric circuit network input unit 12, the layoutdata supplied from layout input unit 13, and the heat circuit networksupplied from heat circuit network conversion unit 16, and supplies theresult to output unit 15.

FIG. 7 shows a processing procedure for an electric circuit simulationperformed in the circuit simulator of this embodiment. In the following,the electric circuit simulation will be described specifically withreference to FIG. 7.

First, initial conditions are set for executing the electric circuitsimulation (step 201). Specifically, the number of elements isdesignated by N; the temperature, voltage, current, and thermalresistance of an n-th element are designated by T(n, k), V(n, k), I(n,k), and Rth(n, k), respectively; the voltage and current of an m-thelement are designated by V(m, k) and I(m, k), respectively; a voltageconvergence determination condition is designated by εv; currentconvergence determination condition is designated by εi; and a thermalresistance convergence determination condition is designated by εr.Variable k is set to 0, and coefficients n, m are respectively set toone. Coefficients n, m are respectively in a range of one or more to Nor less.

After setting the initial conditions, self-heat generation amount Qs(n,k) in the n-th element is calculated on the basis of voltage value V(n,k), current value (n, k) in the n-th element, and thermal resistancevalue Rth(n, k) (step 202), and self-heat generation temperature ΔTs(n,k) at the n-th element is calculated on the basis of self-heatgeneration amount Qs(n, k) and thermal resistance value Rth(n, k) in then-th element (step 203). Further, simultaneously with this processing atsteps 202, 203, or sequentially, heat amount Qi(n, m, k) which flowsfrom the m-th element into the n-th element is calculated on the basisof voltage value V(m, k) and current value I(m, k) in the m-th element(step 204). Then, a countable sum is calculated in a range wherevariable m of heat amount Qi(n, m, k) changes from one to n−1, and in arange where variable m changes from n+1 to N, and heat generationtemperature ΔTi(n, m, k) at the n-th element, caused by a heat amountflowing from the m-th element to the n-th element, is calculated on thebasis of the countable sum and thermal resistance value Rth(n, k) in then-th element (step 205).

Next, temperature T(n, k), self-heat generation temperature ΔTs(n, k),and heat generation temperature ΔTi(n, m, k) of the n-th element areadded to designate the resulting value as element temperature T(n, k+1)of the n-th element (step 206). Then, new voltage value V(n, k+1),current value (n, k+1), and thermal resistance value Rth(n, k+1) arecalculated in the n-th element at element temperature T(n, k+1) (step207), and the value of coefficient n is compared with the value of thenumber N of element (step 208). Here, new voltage value V(n, k+1),current value I(n, k+1), and thermal resistance value Rth(n, k+1) in then-th element are calculated on the basis of data indicative ofpreviously given temperature dependency (voltage/current characteristicsincluding the temperature) of the n-th element.

When it is determined at step 208 that the value of coefficient n isless than number N of elements, coefficient n is incremented by one toproduce new coefficient n, followed by a transition to step 202 and step204 (step 209). When it is determined at step 208 that coefficient n isequal to or more than number N of elements, a countable sum of thedifference between voltage value V(n, k+1) calculated at step 207 andvoltage value V(n, k) in the range of coefficient n from one to N isdesignated as voltage variation EV, a countable sum of the differencebetween current value I(n, k+1) calculated at step 207 and current valueI(n, k) in the range of coefficient n from one to N is designated ascurrent variation EI, and a countable sum of the difference betweenthermal resistance value Rth(n, k+1) calculated at step 207 and thermalresistance value Rth(n, k) in the range of coefficient n from one to Nis designated as thermal resistance value Rth(n, k) (step 210). Then,voltage variation EV is compared with voltage convergence determinationcondition εv, current variation EI is compared with current convergencedetermination condition εi, and thermal resistance variation ER iscompared with thermal resistance convergence determination condition εr,respectively (step 211).

When the value of EV is determined to be larger than the value of εv, orwhen the value of EI is determined to be larger than the value of εi, orwhen the value of ER is determined to be larger than the value of εr atstep 211, the value of variable k is incremented by one to produce newvariable k, followed by a transition to step 202 and step 204 (step212). When it is determined at step 211 that the value of EV is equal toor less than the value of εv, the value of EI is equal to or less thanthe value of εi, and the value of ER is equal to or less than the valueof εr, the simulation processing is terminated.

In the foregoing procedure of simulation processing, the processing atsteps 202-207 is repeatedly executed until n≧N is satisfied at step 208after step 201 has been executed. Then, after step 210 has beenexecuted, the processing at steps 202-210 is repeatedly executed whilechanging each value of voltage value V(n, k), current value I(n, k), andthermal resistance value Rth(n, k) until the respective values of EV,EI, and ER are determined to be equal to or less than the values of theconvergence determination conditions, respectively, at step 211. Throughsuch repeated processing, a voltage, a current, and a temperature can becalculated taking into consideration the influence by respectiveself-heat generation of a plurality of elements which make up thecircuit, and heat generation between the elements.

According to the circuit simulator of this embodiment, in addition tothe effects of the first embodiment, the dependence on temperature withregard to the thermal resistance can also be precisely calculated, thusmaking it possible to precisely calculate a temperature variation of acircuit caused by heat generation to find the current/voltagecharacteristics of an element associated with the temperature variation.Consequently, the circuit simulator of this embodiment enables a precisesimulation of a small semiconductor integrated circuit, and contributesto a reduction in the number of times of re-works and a saving indevelopment cost.

The circuit simulator of this embodiment is an example of the presentinvention, and can be modified in configuration and operation asappropriate. For example, in the processing procedure shown in FIG. 7, astep may be added, before step 201, for deriving thermal resistance atan n-th element using the element shape of the n-th element of thelayout data. In this way, a seamless design can be implemented, forexample, across mask fabrication and a circuit design by derivingthermal resistance value Rth in the n-th element from the element shapeof the layout data.

Alternatively, at step 204, the distance between the n-th element andm-th element is calculated on the basis of the layout data, and heatamount Qi(n, m, k) flowing from the m-th element into the n-th elementmay be derived on the basis of the distance between the elements and onthe basis of voltage value V(m, k) and current value I(m, k) in the m-thelement. In this event, a seamless design can be implemented across maskfabrication and a circuit design.

Alternatively, heat amount Qi(n, m, k) may be represented by Qi(n, m,k)=A×[V(m, k)×I(m, k)], using coefficient A as is the case with thefirst embodiment. In this event, coefficient A may depend on time.According to the use of time-dependent coefficient A, thevoltage/current characteristics of the element can be simulated takinginto consideration the transient response of heat (time transientresponse characteristic). Further, when the current source element shownin FIG. 4 is given and when heat amount Qi(n, m, k) is calculated forthe current source element, coefficient A may be represented by currentgain a of the current source element. In this way, a heat circuitnetwork and an electric circuit network can be precisely andsimultaneously simulated using the electric circuit simulator.

Also, heat amount Qi(n, m, k) may be represented by Qi(n, m, k)=B×[T(m,k)−T(m, 0)] using coefficient B as is the case with the firstembodiment. In this event, coefficient B may also depend on the time. Byusing a coefficient that is dependent on time, the voltage/currentcharacteristics of an element can be simulated taking into considerationthe transient response of heat (time transient response characteristic).Further, when the voltage controlled current source element shown inFIG. 5 is given and when heat amount Qi(n, m, k) is calculated for thisvoltage controlled current source element, coefficient B may berepresented by transconductance g of the voltage controlled currentsource element. In this way, a heat circuit network and an electriccircuit network can be simultaneously and precisely simulated using theelectric circuit simulator.

The electric circuit simulation processing (the electric circuitsimulation processing as shown in FIGS. 2, 3, 7) performed by thecircuit simulator of each embodiment described above is basicallyimplemented by a computer which executes a program. The program may beprovided on a recording medium such as CD-ROM (Compact Disc Read OnlyMemory), DVD (Digital Versatile Disc) or the like, or may be providedthrough a network such as the Internet.

While the present invention has been described with reference to theembodiments, the present invention is not limited to the embodimentsdescribed above. The present invention can be modified in configurationand operation in various ways which can be understood by those skilledin the art without departing from the spirit of the present invention.

This application claims the priority of Japanese Patent Application No.2006-341276 filed on Dec. 19, 2006, the disclosure of which is hereinincorporated by reference in its entirety.

1. A circuit simulator comprising: an electric circuit network inputunit that inputs an electric circuit network that indicates a connectionrelation associated with a plurality of elements which make up asemiconductor integrated circuit; a heat circuit network input unit thatinputs a heat circuit network which is a heat equivalent circuitassociated with the plurality of elements; and a simulation unit thatexecutes an electric circuit simulation for the semiconductor integratedcircuit based on a first element temperature, a first voltage value, afirst current value, and a thermal resistance value, which have been setfor each of the plurality of elements as initial conditions, withreference to the electric circuit network supplied from said electriccircuit network input unit and the heat circuit network supplied fromsaid heat circuit network input unit, wherein said simulation unitcalculates a first heat generation temperature for each of the pluralityof elements, caused by the amount of self-heat generation of said eachelement, based on the first voltage value, first current value, andthermal resistance value of said each element, calculates a second heatgeneration temperature caused by the amount of heat flowing from theother element into said each element based on the first voltage valueand first current value of the other element and the thermal resistancevalue of said each element, calculates a second element temperature ofsaid each element based on the first and second heat generationtemperatures and the first element temperature of said each element, andcalculates a second voltage value and a second current value at saideach element at the second element temperature based on previously givendata indicative of temperature dependency of said each element.
 2. Thecircuit simulator according to claim 1, wherein said simulation unitrepeats a process, said process comprising: calculating the differencebetween the first voltage value and the second voltage value for each ofthe plurality of elements, and calculating a voltage variation which isan addition sum of the differences; calculating the difference betweenthe first current value and the second current value for each of theplurality of elements, and calculating a current variation which is anaddition sum of the differences; changing each value of the firstvoltage value and first current value until both the voltage variationand current variation decrease to previously set convergence conditionvalues or less to calculate the second element temperature for each ofthe plurality of elements; and calculating the second voltage value andsecond current value at the second element temperature.
 3. The circuitsimulator according to claim 1, wherein said simulation unit is providedwith layout data including shape data related to each of the pluralityof elements, and derives the thermal resistance value for each of theplurality of elements using the shape data of an applicable element onthe layout data.
 4. The circuit simulator according to claim 1, whereinsaid simulation unit is provided with layout data including distancedata between each element of the plurality of elements, and calculatesthe second heat generation temperature for each of the plurality ofelements using applicable distance data between elements on the layoutdata instead of using the thermal resistance value.
 5. A circuitsimulator comprising: an electric circuit network input unit that inputsan electric circuit network that indicates of a connection relationassociated with a plurality of elements which make up a semiconductorintegrated circuit; a heat circuit network input unit that inputs a heatcircuit network which is a heat equivalent circuit associated with theplurality of elements; and a simulation unit that executes an electriccircuit simulation for the semiconductor integrated circuit based on afirst element temperature, a first voltage value, a first current value,and a first thermal resistance value, which have been set for each ofthe plurality of elements as initial conditions, with reference to theelectric circuit network supplied from said electric circuit networkinput unit and the heat circuit network supplied from said heat circuitnetwork input unit, wherein said simulation unit calculates a first heatgeneration temperature for each of the plurality of elements, caused bythe amount of self-heat generation of said each element, based on thefirst voltage value, first current value, and first thermal resistancevalue of said each element, calculates a second heat generationtemperature caused by the amount of heat flowing from the other elementinto said each element based on the first voltage value and firstcurrent value of the other element and the first thermal resistancevalue of said each element, calculates a second element temperature ofsaid each element based on the first and second heat generationtemperatures and the first element temperature of said each element, andcalculates a second voltage value, a second current value, and a secondthermal resistance value at said each element at the second elementtemperature based on previously given data indicative of temperaturedependency of said each element.
 6. The circuit simulator according toclaim 5, wherein said simulation unit repeats a process, said processcomprising: calculating the difference between the first voltage valueand the second voltage value for each of the plurality of elements, andcalculating a voltage variation which is an addition sum of thedifferences; calculating the difference between the first current valueand the second current value for each of the plurality of elements, andcalculating a current variation which is an addition sum of thedifferences; calculating the difference between the first thermalresistance value and the second thermal resistance value for each of theplurality of elements, and calculating a thermal resistance variationwhich is an addition sum of the differences; changing each value of thefirst voltage value, first current value, and first thermal resistancevalue until the respective voltage variation, current variation, and thethermal resistance variation decrease to previously set convergencecondition values or less, to calculate the second element temperaturefor each of the plurality of elements; and calculating the secondvoltage value, second current value, and second thermal resistance valueat the second element temperature.
 7. The circuit simulator according toclaim 5, wherein said simulation unit is provided with layout dataincluding shape data related to each of the plurality of elements, andderives the first thermal resistance value for each of the plurality ofelements using the shape data of an applicable element on the layoutdata.
 8. The circuit simulator according to claim 5, wherein saidsimulation unit is provided with layout data including distance databetween each element of the plurality of elements, and calculates thesecond heat generation temperature for each of the plurality of elementsusing applicable distance data between elements on the layout datainstead of using the first thermal resistance value.
 9. The circuitsimulator according to claim 2, wherein: when, the number of theplurality of elements is N, the number of times of repetitions is k forprocessing performed when at least one of the voltage variation andcurrent variation exceeds a previously set convergence condition value,the amount of heat flowing from an m-th element (1≦m≦N) into an n-thelement (1≦n≦N) of the plurality of elements is Qi(n, m, k), and thefirst voltage value and first current value of the m-th element are V(m,k) and I(m, k), respectively, said Qi(n, m, k) is given by:Qi(n, m, k)=A×[V(m, k)×I(m, k)] where A is a coefficient.
 10. Thecircuit simulator according to claim 9, wherein said coefficient A istime dependent.
 11. The circuit simulator according to claim 9, whereinsaid n-th element is a current source element, and said coefficient A isa current gain of said current source element.
 12. The circuit simulatoraccording to claim 2, wherein: when, the number of the plurality ofelements is N, the number of times of repetitions is k for processingperformed when at least one of the voltage variation and currentvariation exceeds a previously set convergence condition value, theamount of heat flowing from an m-th element (1≦m≦N) into an n-th element(1≦n≦N) of the plurality of elements is Qi(n, m, k), an elementtemperature at the m-th element is T(m, 0) when the k is zero, and theelement temperature at the m-th element is T(m, k) when the k is otherthan zero, said Qi(n, m, k) is given by:Qi(n, m, k)=B×[T(m, k)−T(m, 0)] where B is a coefficient.
 13. Thecircuit simulator according to claim 12, wherein said coefficient B istime dependent.
 14. The circuit simulator according to claim 12, whereinsaid n-th element is a voltage controlled current source element, andsaid coefficient B is a transconductance of said voltage controlledcurrent source element.
 15. A method of simulating a semiconductorintegrated circuit comprised of a plurality of elements, said methodcomprising: executing an electric circuit simulation for saidsemiconductor integrated circuit based on a first element temperature, afirst voltage value, a first current value, and a thermal resistancevalue set as initial conditions for each of the plurality of elements,with reference to an electric circuit network that indicates aconnection relation associated with the plurality of elements and a heatcircuit network which is a heat equivalent circuit associated with theplurality of elements, wherein said executing a electric circuitsimulation includes calculating a first heat generation temperature foreach of the plurality of elements, caused by the amount of self-heatgeneration of said each element, based on the first voltage value, firstcurrent value, and thermal resistance value of said each element,calculating a second heat generation temperature caused by the amount ofheat flowing from the other element into said each element based on thefirst voltage value and first current value of the other element and thethermal resistance value of said each element, calculating a secondelement temperature of said each element based on the first and secondheat generation temperatures and the first element temperature of saideach element, and calculating a second voltage value and a secondcurrent value at said each element at the second element temperaturebased on previously given data indicative of temperature dependency ofsaid each element.
 16. The circuit simulation method according to claim15, wherein said executing an electric circuit simulation includesrepeating a process, said process comprising: calculating the differencebetween the first voltage value and the second voltage value for each ofthe plurality of elements, and calculating a voltage variation which isan addition sum of the differences; calculating the difference betweenthe first current value and the second current value for each of theplurality of elements, and calculating a current variation which is anaddition sum of the differences; changing each value of the firstvoltage value and first current value until both the voltage variationand current variation decrease to previously set convergence conditionvalues or less to calculate the second element temperature for each ofthe plurality of elements; and calculating the second voltage value andsecond current value at the second element temperature.
 17. A method ofsimulating a semiconductor integrated circuit comprised of a pluralityof elements, said method comprising: executing an electric circuitsimulation for said semiconductor integrated circuit based on a firstelement temperature, a first voltage value, a first current value, and afirst thermal resistance value set as initial conditions for each of theplurality of elements, with reference to an electric circuit networkthat indicates a connection relation associated with the plurality ofelements and a heat circuit network which is a heat equivalent circuitassociated with the plurality of elements, wherein said executing anelectric circuit simulation includes: calculating a first heatgeneration temperature for each of the plurality of elements, caused bythe amount of self-heat generation of said each element, based on thefirst voltage value, first current value, and first thermal resistancevalue of said each element, calculating a second heat generationtemperature caused by the amount of heat flowing from the other elementinto said each element based on the first voltage value and firstcurrent value of the other element and the first thermal resistancevalue of said each element, calculating a second element temperature ofsaid each element based on the first and second heat generationtemperatures and the first element temperature of said each element, andcalculating a second voltage value, a second current value, and a secondthermal resistance value at said each element at the second elementtemperature based on previously given data indicative of temperaturedependency of said each element.
 18. The circuit simulation methodaccording to claim 17, wherein said executing an electric circuitsimulation includes repeating a process, said process comprising:calculating the difference between the first voltage value and thesecond voltage value for each of the plurality of elements, andcalculating a voltage variation which is an addition sum of thedifferences; calculating the difference between the first current valueand the second current value for each of the plurality of elements, andcalculating a current variation which is an addition sum of thedifferences; calculating the difference between the first thermalresistance value and the second thermal resistance value for each of theplurality of elements, and calculating a thermal resistance variationwhich is an addition sum of the differences; changing each value of thefirst voltage value, first current value, and first thermal resistancevalue until the respective voltage variation, current variation, and thethermal resistance variation decrease to previously set convergencecondition values or less, to calculate the second element temperaturefor each of the plurality of elements; and calculating the secondvoltage value, second current value, and second thermal resistance valueat the second element temperature.
 19. A recording medium recorded witha program for causing a computer to execute a process for executing anelectric circuit simulation for a semiconductor integrated circuit basedon a first element temperature, a first voltage value, a first currentvalue, and a thermal resistance value set as initial conditions for eachof a plurality of elements which make up said semiconductor integratedcircuit, with reference to an electric circuit network indicative of aconnection relation associated with the plurality of elements and a heatcircuit network which is a heat equivalent circuit associated with theplurality of elements, wherein said process for executing an electriccircuit simulation includes processing for calculating a first heatgeneration temperature for each of the plurality of elements, caused bythe amount of self-heat generation of said each element, based on thefirst voltage value, first current value, and thermal resistance valueof said each element, processing for calculating a second heatgeneration temperature caused by the amount of heat flowing from theother element into said each element based on the first voltage valueand first current value of the other element and the thermal resistancevalue of said each element, processing for calculating a second elementtemperature of said each element based on the first and second heatgeneration temperatures and the first element temperature of said eachelement, and processing for calculating a second voltage value and asecond current value at said each element at the second elementtemperature based on previously given data indicative of temperaturedependency of said each element.
 20. The recording medium according toclaim 19, wherein said process for executing an electric circuitsimulation includes repeating a process which comprises: calculating thedifference between the first voltage value and the second voltage valuefor each of the plurality of elements, and calculating a voltagevariation which is an addition sum of the differences; calculating thedifference between the first current value and the second current valuefor each of the plurality of elements, and calculating a currentvariation which is an addition sum of the differences; changing eachvalue of the first voltage value and first current value until both thevoltage variation and current variation decrease to previously setconvergence condition values or less, to calculate the second elementtemperature for each of the plurality of elements; and calculating thesecond voltage value and second current value at the second elementtemperature.
 21. A recording medium recorded with a program for causinga computer to execute a process for executing an electric circuitsimulation for a semiconductor integrated circuit based on a firstelement temperature, a first voltage value, a first current value, and afirst thermal resistance value set as initial conditions for each of aplurality of elements which make up said semiconductor integratedcircuit, with reference to an electric circuit network indicative of aconnection relation associated with the plurality of elements and a heatcircuit network which is a heat equivalent circuit associated with theplurality of elements, wherein said process for executing an electriccircuit simulation includes processing for calculating a first heatgeneration temperature for each of the plurality of elements, caused bythe amount of self-heat generation of said each element, based on thefirst voltage value, first current value, and first thermal resistancevalue of said each element, processing for calculating a second heatgeneration temperature caused by the amount of heat flowing from theother element into said each element based on the first voltage valueand first current value of the other element and the first thermalresistance value of said each element, processing for calculating asecond element temperature of said each element based on the first andsecond heat generation temperatures and the first element temperature ofsaid each element, and processing for calculating a second voltagevalue, a second current value, and a second thermal resistance value atsaid each element at the second element temperature based on previouslygiven data indicative of temperature dependency of said each element.22. The recording medium according to claim 21, wherein said process forexecuting an electric circuit simulation includes repeating a processwhich comprises: calculating the difference between the first voltagevalue and the second voltage value for each of the plurality ofelements, and calculating a voltage variation which is an addition sumof the differences; calculating the difference between the first currentvalue and the second current value for each of the plurality ofelements, and calculating a current variation which is an addition sumof the differences; calculating the difference between the first thermalresistance value and the second thermal resistance value for each of theplurality of elements, and calculating a thermal resistance variationwhich is an addition sum of the differences; changing each value of thefirst voltage value, first current value, and first thermal resistancevalue until the respective voltage variation, current variation, and thethermal resistance variation decrease to previously set convergencecondition values or less, to calculate the second element temperaturefor each of the plurality of elements; and calculating the secondvoltage value, second current value, and second thermal resistance valueat the second element temperature.
 23. The circuit simulator accordingto claim 6, wherein: when, the number of the plurality of elements is N,the number of times of repetitions is k for processing performed when atleast one of the voltage variation and current variation exceeds apreviously set convergence condition value, the amount of heat flowingfrom an m-th element (1≦m≦N) into an n-th element (1≦n≦N) of theplurality of elements is Qi(n, m, k), and the first voltage value andfirst current value of the m-th element are V(m, k) and I(m, k),respectively, said Qi(n, m, k) is given by:Qi(n, m, k)=A×[V(m, k)×I(m, k)] where A is a coefficient.
 24. Thecircuit simulator according to claim 23, wherein said coefficient A istime dependent.
 25. The circuit simulator according to claim 23, whereinsaid n-th element is a current source element, and said coefficient A isa current gain of said current source element.
 26. The circuit simulatoraccording to claim 6, wherein: when, the number of the plurality ofelements is N, the number of times of repetitions is k for processingperformed when at least one of the voltage variation and currentvariation exceeds a previously set convergence condition value, theamount of heat flowing from an m-th element (1≦m≦N) into an n-th element(1≦n≦N) of the plurality of elements is Qi(n, m, k), an elementtemperature at the m-th element is T(m, 0) when the k is zero, and theelement temperature at the m-th element is T(m, k) when the k is otherthan zero, said Qi(n, m, k) is given by:Qi(n, m, k)=B×[T(m, k)−T(m, 0)] where B is a coefficient.
 27. Thecircuit simulator according to claim 26, wherein said coefficient B istime dependent.
 28. The circuit simulator according to claim 26, whereinsaid n-th element is a voltage controlled current source element, andsaid coefficient B is a transconductance of said voltage controlledcurrent source element.